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# An infinite geometric series has common ratio $-1/5$ and sum $16.$ What is the first term of the series?

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64
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An infinite geometric series has common ratio $$-\frac{1}{5}$$ and sum $$16$$ What is the first term of the series?

Sep 6, 2021

#1
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From the formula, the first term is a = 64/5.

Sep 6, 2021
#2
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Its 96/5. The formula for sum of an infinite geometric series is      A1/1-r         Where  Ais the first term in the series and r is the common ratio. Plugging in your values, you have  A1/1-(-1/5)=16------------>  A1/(6/5)=16 Solving for  A1 you get 96/5. No clue where my guy got 64/5 from.

Sep 6, 2021
edited by Guest  Sep 6, 2021